© 2018 The Author(s) Published by the Royal Society. All rights reserved. This paper explores the question of ethical governance for robotics and artificial intelligence (AI) systems. We outline a roadmap-which links a number of elements, including ethics, standards, regulation, responsible research and innovation, and public engagement-as a framework to guide ethical governance in robotics and AI. We argue that ethical governance is essential to building public trust in robotics and AI, and conclude by proposing five pillars of good ethical governance. This article is part of the theme issue 'Governing artificial intelligence: ethical, legal, and technical opportunities and challenges'.